Beshear, who challenged McConnell unsuccessfully in 1996, said he expects a credible Democratic candidate to step forward.

"I have no interest in running for that or any other office," he told reporters in a Capitol press conference.

The name mentioned most in recent weeks as a challenger to McConnell has been actress Ashley Judd, well-known in Kentucky because of her success in Hollywood and because of her famous mother and sister, country music stars Naomi and Wynonna Judd.

"Whether or not she will end up in the elective arena or not, I don't' have any idea," Beshear said. "I think it's too early to know what direction she will go or what direction a lot of other people who are thinking about it will go."

Ashley Judd, a former Kentucky resident now living in Tennessee, hasn't ruled out a run. But neither has she said anything to suggest that she would enter the race.

Her publicist said Tuesday nothing has changed since the actress released a statement last month saying she was honored to be mentioned as a potential candidate.

Beshear is the latest of several top tier Democrats who have said they won't challenge McConnell. That list includes Attorney General Jack Conway and former state Auditor Crit Luallen.

"I don't have any inside information on who might be thinking seriously about running at this point," the governor said. "I think a lot of people are looking at it and thinking about it, but whether they will get serious about it is yet to be determined."

Beshear offered no names of potential Democratic candidates.

"I feel confident that we will have a credible candidate," he said. "It will be a difficult race as we all know because one of the senator's strongest assets is his ability to raise money. He's always had that ability, and has developed it to the highest art form."

With the election still nearly two years away, McConnell has banked more than $6.8 million. He spent some $20 million on his last election to defeat wealthy Louisville businessman Bruce Lunsford by 6 percentage points.